We show that different classes of topological order can be distinguished by
the dynamical symmetry algebra of edge excitations. Fundamental topological
order is realized when this algebra is the largest possible, the algebra of
quantum area-preserving diffeomorphisms, called W1+∞​. We argue that
this order is realized in the Jain hierarchy of fractional quantum Hall states
and show that it is more robust than the standard Abelian Chern-Simons order
since it has a lower entanglement entropy due to the non-Abelian character of
the quasi-particle anyon excitations. These behave as SU(m) quarks, where m
is the number of components in the hierarchy. We propose the topological
entanglement entropy as the experimental measure to detect the existence of
these quantum Hall quarks. Non-Abelian anyons in the ν=2/5 fractional
quantum Hall states could be the primary candidates to realize qbits for
topological quantum computation.Comment: 5 pages, no figures, a few typos corrected, a reference adde